The Kyoto Protocol was signed in 1997, and required countries to start reducing their carbon emissions. The protocol became enforceable in February 2005. In 2004, the mean $\mathrm{CO} 2$ emission was 4.87 metric tons per capita. In 2010, the $\mathrm{CO} 2$ emissions for a random sample of 47 countries were collected. Is there enough evidence to show that the mean $\mathrm{CO} 2$ emission is lower in 2010 than in 2004 ? State the random variable, population parameter, and hypotheses. a) The symbol for the random variable involved in this problem is ?v The wording for the random variable in context is as follows: Select an answer b) The symbol for the parameter involved in this problem is ?v The wording for the parameter in context is as follows: Select an answer c) Fill in the correct null and alternative hypotheses: \[ \begin{array}{l} H_{0}: \text { ?v? ? } \\ H_{A}: \text { ?v?ฯ } \\ \end{array} \]
Solution
Step 1 ：This is a hypothesis testing problem. We are trying to determine if there is a significant difference in the mean CO2 emissions between 2004 and 2010.
Step 2 ：The random variable in this case would be the CO2 emissions for a random sample of 47 countries in 2010. The symbol for the random variable involved in this problem is X.
Step 3 ：The population parameter would be the mean CO2 emissions in 2004, which is given as 4.87 metric tons per capita. The symbol for the parameter involved in this problem is μ.
Step 4 ：The null hypothesis (H0) would be that the mean CO2 emissions in 2010 is equal to the mean CO2 emissions in 2004. The alternative hypothesis (HA) would be that the mean CO2 emissions in 2010 is less than the mean CO2 emissions in 2004.
Step 5 ：The null and alternative hypotheses are: \[\begin{array}{l} H_{0}: \mu = 4.87 \\ H_{A}: \mu < 4.87 \end{array}\]
